Regional Economic Birch-Swinnerton-Dyer Modelling: A Local-to-Global Framework for Structural Rank Formation, Corridor Stress and World-Economy Calibration

This study develops a regional economic Birch-Swinnerton-Dyer-inspired framework for measuring the world economy as a local-to-global structural system rather than as a set of isolated GDP aggregates. The framework does not claim to prove, test or replicate the classical Birch-Swinnerton-Dyer conjecture. Instead, it translates its local-to-global measurement logic into a transparent economic analogue in which public macro-regional anchors are transformed into systemic-stress components, weighted regional-network structure, economic curve coefficients, discriminant diagnostics, finite-state trace analogues, Euler-factor analogues, a constructed economic L-function and an L-order measure. The empirical universe consists of a World normalisation anchor and ten macro-regional/corridor nodes, with an N = 150 regional-year closure layer used for calibration, robustness diagnostics and claim discipline. The central result is that local regional reductions, represented by finite-state regimes rather than literal arithmetic reductions over finite fields, contain measurable information about structural economic rank formation. Structural rank is constructed from productive, Hodge-flow, network and agentic components and is compared with the L-order analogue through rank gaps, agreement diagnostics, sensitivity checks and placebo logic. The model further introduces regulator, Tamagawa-type friction, torsion, BridgeStress, scenario-threshold and action-concentration diagnostics to distinguish output mass, absorption capacity, locked capacity, corridor leverage and systemic transmission exposure. Results support a strong calibrated measurement claim: local regional signals and Euler-factor information are informative about global structural rank under a disciplined analogue architecture. At the same time, robust inference and external proxy layers are interpreted conservatively; weak p-values, small regional clusters, circularity risk and directional external screening are not upgraded into causal or theorem-level confirmation. The contribution is therefore methodological and empirical: a reproducible regional BSD-inspired measurement architecture for structural rank, corridor stress and local-to-global macroeconomic calibration.